An autostereoscopic three-dimensional display system for surgical robotics has an autostereoscopic three-dimensional display configured to receive and display video from a surgical robotics camera, and a first sensor assembly and a second sensor assembly. A processor is configured to detect and track an eye position or a head position of a user relative to the display based on processing output data of the first sensor assembly, and to detect and track a gaze of the user based on processing output data of the second sensor assembly. The processor further is configured to modify or control an operation of the display system based on the detected gaze of the user. A spatial relationship of the display also can be automatically adjusted in relation to the user based on the detected eye or head position of the user to optimize the user's visualization of three-dimensional images on the display.